code: def test_ddm_ilu_split():
      U = []
      L = []
      Uexp = []
      Lexp = []
      swaps = ddm_ilu_split(L, U, QQ)
      assert U == Uexp
      assert L == Lexp
      assert swaps == []
  
      U = [[]]
      L = [[QQ(1)]]
      Uexp = [[]]
      Lexp = [[QQ(1)]]
      swaps = ddm_ilu_split(L, U, QQ)
      assert U == Uexp
      assert L == Lexp
      assert swaps == []
  
      U = [[QQ(1), QQ(2)], [QQ(3), QQ(4)]]
      L = [[QQ(1), QQ(0)], [QQ(0), QQ(1)]]
      Uexp = [[QQ(1), QQ(2)], [QQ(0), QQ(-2)]]
      Lexp = [[QQ(1), QQ(0)], [QQ(3), QQ(1)]]
      swaps = ddm_ilu_split(L, U, QQ)
      assert U == Uexp
      assert L == Lexp
      assert swaps == []
  
      U = [[QQ(1), QQ(2), QQ(3)], [QQ(4), QQ(5), QQ(6)]]
      L = [[QQ(1), QQ(0)], [QQ(0), QQ(1)]]
      Uexp = [[QQ(1), QQ(2), QQ(3)], [QQ(0), QQ(-3), QQ(-6)]]
      Lexp = [[QQ(1), QQ(0)], [QQ(4), QQ(1)]]
      swaps = ddm_ilu_split(L, U, QQ)
      assert U == Uexp
      assert L == Lexp
      assert swaps == []
  
      U = [[QQ(1), QQ(2)], [QQ(3), QQ(4)], [QQ(5), QQ(6)]]
      L = [
          [QQ(1), QQ(0), QQ(0)],
          [QQ(0), QQ(1), QQ(0)],
          [QQ(0), QQ(0), QQ(1)],
      ]
      Uexp = [[QQ(1), QQ(2)], [QQ(0), QQ(-2)], [QQ(0), QQ(0)]]
      Lexp = [
          [QQ(1), QQ(0), QQ(0)],
          [QQ(3), QQ(1), QQ(0)],
          [QQ(5), QQ(2), QQ(1)],
      ]
      swaps = ddm_ilu_split(L, U, QQ)
      assert U == Uexp
      assert L == Lexp
      assert swaps == []
  
file_path: sympy/sympy/polys/matrices/tests/test_dense.py
imports: from sympy.testing.pytest import raises
  from sympy.polys import ZZ, QQ
  from sympy.polys.matrices.ddm import DDM
  from sympy.polys.matrices.dense import ddm_transpose, ddm_iadd, ddm_isub, ddm_ineg, ddm_imatmul, ddm_imul, ddm_irref, ddm_idet, ddm_iinv, ddm_ilu, ddm_ilu_split, ddm_ilu_solve, ddm_berk
  from sympy.polys.matrices.exceptions import DMDomainError, DMNonInvertibleMatrixError, DMNonSquareMatrixError, DMShapeError
label_desc: Use image node_id 11 for calling a global function with example usage: test_ddm_ilu_split() without return types